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I've a circular array of eight FM antennas. I'm doing digital beamforming to form eight beams with the following beam patterns: enter image description here

The objective is to reduce my side lobes even further, and to get narrower main beam. What I'm interested in to know if it is possible to take two adjacent beams, and do another step of beamforming, i.e., considering them as if coming from two antenna array with the beam pattern shown in the figure. I don't know how to incorporate the beam pattern into the standard set of equations for beamforming, as I think an omni-directional antenna is assumed. Any directions, suggestions are welcome.

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  • $\begingroup$ Welcome. I think this is a good question. $\endgroup$ – Jason R May 21 '14 at 2:20
  • $\begingroup$ Can you please describe in detail how you formed the current beams? Are you using ALL 8 sensors per beam? $\endgroup$ – Tarin Ziyaee May 22 '14 at 14:04
  • $\begingroup$ Yes, currently, I'm using all eight sensors per beam. $\endgroup$ – learner May 23 '14 at 10:07
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For now I will focus on the conceptual, pending feedback from you:

What I'm interested in to know if it is possible to take two adjacent beams, and do another step of beamforming,

The answer to this is yes, this is possible to do, and this is done in many beamforming applications. Think about it like this: All beamforming is really doing, is undoing the delays your signals exhibit (by virtue of different sensors at different locations), and summing the result. (Example: Delay-And-Sum beamformer). But in what order you undo the delays, before summing doesn't matter.

Thus, the beamformed result of a sub-group of sensors can be considered as one 'element', and the beamformed result of another sub-group of sensors, another 'element', and then both 'element's' outputs are beamformed.

In other words, first we remove the effects of the delays in one sub-array. Then we remove the effects of the delays in the other sub-array. At this point, both signal outputs might still have a delay relative to each other. So then again, both those inputs can be beamformed again. You can keep doing this ad infinitum.

The objective is to reduce my side lobes even further, and to get narrower main beam.

If this is the objective, then the only way to reduce your main lobe width is to sample the spatial field with more sensors. This is the direct analogue to time-domain sampling. If we want greater frequency resolution (smaller main lobe width in the DFT analysis), we need to process a greater number of samples in time. Similarly, if we would like a smaller main-lobe width of our spatial spectra, we need to sample the spatial field with more sensors.

EDIT: Taking from the above, if you want to decrease your mainlobe width, you need more spatial samples. However if you want to reduce your sidelobes, then you would use a variety of windowing/shading functons. (Each of those functions will give you a slight increase in mainlobe width, but that is the price to pay). I am not sure what shading you have used for the above plots, but that will be good to know.

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  • $\begingroup$ I expect that at least I'll get lower side lobes. But what will the final beam pattern look like? Are there any directions on that? $\endgroup$ – learner May 22 '14 at 5:56
  • $\begingroup$ Why do you expect lower sidelobes? We can attain lower sidelobes based on the shading/windowing function used. What shading did you use on the current beamformer? $\endgroup$ – Tarin Ziyaee May 22 '14 at 14:00
  • $\begingroup$ I'm computing the coefficients using LS optimization, forcing the first side lobe to be around -25dB. Can we get better than that? $\endgroup$ – learner May 23 '14 at 10:11
  • $\begingroup$ @learner Have you considered Dolph-Chebychev shading? I can write about it if you have not. With DC shading, you can specify your minimum sidelobe levels, (eg, -30 dB, -40 db, etc). The sidelobes are solved using the minimax constraint so they will all have a maximum level of this minimal amount. Shoot me an email if you need the code, I have it lying around somewhere. $\endgroup$ – Tarin Ziyaee May 24 '14 at 16:12
  • $\begingroup$ That seems to be a great idea. Actually, I've used Dolph-Chebychev in past, just forgot about them. I'll try them out in coming days and share the results. $\endgroup$ – learner May 24 '14 at 16:50

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